Hard-Trace First-Order Residual Learning for Coupled Stokes-Brinkman-Darcy Flow
Abstract
Stokes-Brinkman-Darcy (SBD) models connect free flow and porous flow through a Brinkman layer of finite thickness. The proposed method for solving these coupled equations consists of a mixed first-order formulation, shared interface traces and hard traction constraints, and a pressure correction based on boundary mass balance. Independent stresses, Darcy flux and pressure-gradient auxiliaries avoid second derivatives of network outputs. Boundary liftings and shared traces impose exterior and interface kinematic conditions exactly, while a stress map enforces native Brinkman-Darcy force balance. An integral momentum relation determines the pressure correction after training, without reference-pressure labels. Across two manufactured solutions and three permeabilities, mean corrected upper-pressure relative L2 errors range from 0.87% to 2.58%; correction reduces both upper-pressure L2 errors and the full Brinkman-pressure H1 error in every run. Paired controls assess the contributions of interface sharing and traction enforcement. A non-manufactured filtration problem tests mixed-boundary adaptation against an independently refined finite-element reference, with all four runs satisfying the prescribed field and physical-consistency criteria.
Related
- From Navier-Stokes to Measure-Valued Euler-Brinkman Equations: Homogenization in the Inviscid Limit
- Elucidating the Conformal Structure of the Brinkman Penalisation Method for Geometry-Adapted, Structure-Preserving Operator Learning of Hamiltonian PDEs
- Finite-Time Blowup for Navier-Stokes with Smooth Forcing, Part II: Residual Correction via Oscillatory Pulses
- A Two-Residual Compactness Framework for Suitable Navier–Stokes Limits
- Global well-posedness for the compressible Navier-Stokes equations with vacuum and smallness on coefficient-coupled scaling invariant quantity
BibTeX
@misc{liu2026hardtrace,
title = {{Hard-Trace First-Order Residual Learning for Coupled Stokes-Brinkman-Darcy Flow}},
author = {Zefeng Liu and Hongxing Rui},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36793},
eprint = {2609.36793},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36793},
}
RIS
TY - UNPB
TI - Hard-Trace First-Order Residual Learning for Coupled Stokes-Brinkman-Darcy Flow
AU - Zefeng Liu
AU - Hongxing Rui
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.36793
UR - https://arxiv.org/abs/2609.36793
AB - Stokes-Brinkman-Darcy (SBD) models connect free flow and porous flow through a Brinkman layer of finite thickness. The proposed method for solving these coupled equations consists of a mixed first-order formulation, shared interface traces and hard traction constraints, and a pressure correction based on boundary mass balance. Independent stresses, Darcy flux and pressure-gradient auxiliaries avoid second derivatives of network outputs. Boundary liftings and shared traces impose exterior and interface kinematic conditions exactly, while a stress map enforces native Brinkman-Darcy force balance. An integral momentum relation determines the pressure correction after training, without reference-pressure labels. Across two manufactured solutions and three permeabilities, mean corrected upper-pressure relative L^2 errors range from 0.87% to 2.58%; correction reduces both upper-pressure L^2 errors and the full Brinkman-pressure H^1 error in every run. Paired controls assess the contributions of interface sharing and traction enforcement. A non-manufactured filtration problem tests mixed-boundary adaptation against an independently refined finite-element reference, with all four runs satisfying the prescribed field and physical-consistency criteria.
ER -